Seven people were killed and at least 21 injured in a brazen daylight drive-by mass shooting in the West Texas cities of Midland and Odessa on Saturday, as a gunman drove on the highways and streets opening fire on residents, motorists and shoppers, the authorities said.

The attack at the start of Labour Day weekend terrified sister cities 32km apart with a combined population of 263,000, less than a month after gunmen killed 31 people in El Paso and Dayton, Ohio, in back-to-back massacres.

The chief of the Odessa police department, Michael Gerke, said at a news conference on Saturday that the attack had begun after a traffic stop. The gunman fled the police and hijacked a postal truck, firing at civilians as he made his way into Odessa.

Reuters quoted Gerke as saying that the suspect was known to him, but the officer declined to comment on a motive for the shootings.

Three law enforcement officers and a toddler were among those wounded, before the police shot and killed the gunman, a man in his mid-30s, near a movie theatre on the outskirts of Odessa. The police said the gunman’s motive was not immediately clear.

Police officers and state troopers warded drivers off the highways as businesses across the two cities shut their doors. Universities went on lockdown. A television station in Odessa evacuated its studio while its reporters were covering the breaking news live on the air.

President Donald Trump said background checks on gun purchasers would not have prevented recent gun violence in the country. He said he would be working with Democrats and Republicans on gun legislation when Congress returns this month.

“I think Congress has got a lot of thinking to do frankly. They’ve been doing a lot of work,” Trump said. “I think you’re going to see some interesting things coming along.”

Trump said at the White House that “for the most part, as strong as you make your background checks, they would not have stopped any of it”.

Trump called the Texas gunman “a very sick person”.

Odessa police officials said the incident began late Saturday afternoon at 3.25pm, when a state trooper on Interstate 20 between Midland and Odessa tried to pull the suspect over. The driver opened fire on the state trooper and fled westbound on the highway, shooting at a person at I-20 and east Loop 338. From there, the suspect “proceeded on a shooting spree in the City of Odessa” and stole a postal truck, the Odessa police said in a statement.

The suspect then drove to the Cinergy movie theatre on Highway 191, shooting an Odessa officer and a Midland officer. Officers returned fire, killing the suspect, the authorities said.

Mayor Jerry Morales of Midland said a rifle had been used in the attack.

Junior Bejarano, 20, a worker at the Twin Peaks restaurant in Odessa, had just finished cleaning a table when he heard a gunshot outside

at about 4.30pm. “It was chaos in a matter of seconds,” he said. “People were screaming, flipping chairs, dropping plates.”

A few minutes later, he and other workers walked outside and saw several cars with bullet holes at a nearby intersection, in the turning lane of E. 42nd Street near Parkway Boulevard. He heard a woman screaming and ran to her car with his co-workers.

Inside, he said he saw a baby girl in a car seat whose face, shirt and lap were covered in blood.